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*The author of this computation has been verified*

R Software Module: /rwasp_structuraltimeseries.wasp (opens new window with default values)

Title produced by software: Structural Time Series Models

Date of computation: Tue, 21 Dec 2010 12:42:27 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve.htm/, Retrieved Tue, 21 Dec 2010 13:41:08 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

104,31 103,88 103,88 103,86 103,89 103,98 103,98 104,29 104,29 104,24 103,98 103,54 103,44 103,32 103,3 103,26 103,14 103,11 102,91 103,23 103,23 103,14 102,91 102,42 102,1 102,07 102,06 101,98 101,83 101,75 101,56 101,66 101,65 101,61 101,52 101,31 101,19 101,11 101,1 101,07 100,98 100,93 100,92 101,02 101,01 100,97 100,89 100,62 100,53 100,48 100,48 100,47 100,52 100,49 100,47 100,44

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Structural Time Series Model
t	Observed	Level	Slope	Seasonal	Stand. Residuals
1	104.31	104.31	0	0	0
2	103.88	103.902294705550	-0.0235502905421562	-0.0222947055497816	-1.68396802191647
3	103.88	103.902212705130	-0.0230627915483656	-0.0222127051305003	0.160576516216919
4	103.86	103.882202348102	-0.0229743379049404	-0.0222023481025030	0.0207960922739162
5	103.89	103.912029756396	-0.0210390066673808	-0.0220297563956681	0.358271067967188
6	103.98	104.001683756457	-0.0161992955968004	-0.0216837564565165	0.748215093703513
7	103.98	104.001635802637	-0.0153894375142909	-0.0216358026373737	0.108789580305062
8	104.29	104.310726263410	0.00274825088015736	-0.0207262634095379	2.17859634360554
9	104.29	104.310733478046	0.0025810502502226	-0.0207334780458504	-0.0183507695207754
10	104.24	104.260862496924	-0.000853205935104232	-0.0208624969238806	-0.350259632538984
11	103.98	104.001454362635	-0.0187878521408545	-0.0214543626347393	-1.72266317912536
12	103.54	103.562346559576	-0.0493539922474934	-0.0223465595762711	-2.79492399348178
13	103.44	103.293242011366	-0.0605653637776451	0.146757988633870	-1.73779670925153
14	103.32	103.331042251593	-0.0519801085368243	-0.0110422515933838	0.555141601417225
15	103.3	103.311022702522	-0.0494380504621622	-0.0110227025217995	0.211408498502653
16	103.26	103.271017400811	-0.0486704764988985	-0.0110174008112351	0.0623290479251919
17	103.14	103.151054148554	-0.0545820478318245	-0.0110541485537382	-0.470664016636422
18	103.11	103.121042550360	-0.0525127744926746	-0.0110425503598981	0.162088201379941
19	102.91	102.921106203583	-0.0650887714572062	-0.0111062035831994	-0.971916856400752
20	103.23	103.240954328097	-0.0319019609830202	-0.0109543280968609	2.53640811558381
21	103.23	103.240942840120	-0.0291284056495086	-0.0109428401203158	0.21003656624671
22	103.14	103.150962840525	-0.0344591376692731	-0.0109628405248079	-0.40062819514297
23	102.91	102.921021428520	-0.0516863719727084	-0.0110214285201618	-1.2865862156552
24	102.42	102.431141128595	-0.0904939968173886	-0.0111411285950175	-2.88324803452654
25	102.1	102.041870481085	-0.115736024969886	0.05812951891548	-2.14835894388426
26	102.07	102.073119677213	-0.102383469934942	-0.00311967721273393	0.881819353261513
27	102.06	102.063117251125	-0.094121432454439	-0.00311725112524153	0.60740502226227
28	101.98	101.983116912324	-0.0928555399991643	-0.00311691232419478	0.0928351410039142
29	101.83	101.833118160191	-0.0979881685703347	-0.00311816019072596	-0.375634958031822
30	101.75	101.753117802721	-0.096369889170432	-0.00311780272060873	0.118234496644265
31	101.56	101.563119495771	-0.104804432737705	-0.00311949577064302	-0.615381067835623
32	101.66	101.663116126409	-0.0863345323848052	-0.00311612640918814	1.34599737485727
33	101.65	101.653114983941	-0.0794441640191125	-0.00311498394129133	0.501656293120192
34	101.61	101.613114446924	-0.0758810333994267	-0.00311444692445935	0.259209976183802
35	101.52	101.523114621774	-0.0771572452658088	-0.00311462177353093	-0.0927808640347435
36	101.31	101.313116118117	-0.0891710819846183	-0.00311611811704867	-0.8729356750975
37	101.19	101.164255139333	-0.0944947635939917	0.0257448606668044	-0.416615268446897
38	101.11	101.111885695164	-0.0906823212614798	-0.00188569516434792	0.259491666821823
39	101.1	101.101891691181	-0.0833773850690747	-0.00189169118054432	0.530149371816324
40	101.07	101.071895291033	-0.0785435153969892	-0.00189529103318753	0.350729359183862
41	100.98	100.981894588374	-0.0795812144845533	-0.00189458837432693	-0.0752769647514083
42	100.93	100.931896238314	-0.0769014032168808	-0.00189623831407626	0.194367357401417
43	100.92	100.921899631758	-0.0708399077083481	-0.00189963175764587	0.439581847152546
44	101.02	101.021907512070	-0.0553595680164641	-0.00190751206959326	1.12251338795001
45	101.01	101.011909414759	-0.0512490306604136	-0.00190941475868671	0.298036319387071
46	100.97	100.971909843856	-0.0502295554935866	-0.00190984385588771	0.0739118026397467
47	100.89	100.891908811178	-0.0529277497666185	-0.00190881117785979	-0.195606237866223
48	100.62	100.621901963855	-0.0726027157772648	-0.00190196385523712	-1.42626624398634
49	100.53	100.512961758190	-0.0758756655620918	0.0170382418103744	-0.249921541121885
50	100.48	100.481172369972	-0.071893471025049	-0.00117236997202315	0.275517192751225
51	100.48	100.481178342147	-0.0653758733014334	-0.00117834214649636	0.472369066887793
52	100.47	100.471182513954	-0.0603556698666559	-0.00118251395444556	0.36384159413811
53	100.52	100.521190074026	-0.0503511181441277	-0.00119007402650279	0.725080618390734
54	100.49	100.491191341815	-0.0485061319441162	-0.00119134181538184	0.133714907349267
55	100.47	100.471192956636	-0.0459218215221221	-0.00119295663560042	0.187296545105111
56	100.44	100.441193776809	-0.0444783759456416	-0.00119377680910751	0.104612640271396

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/1j9k01292935343.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/1j9k01292935343.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/2c01l1292935343.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/2c01l1292935343.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/3c01l1292935343.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/3c01l1292935343.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/449i61292935343.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/449i61292935343.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/549i61292935343.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/21/t1292935262ry9adwh7s7vd6ve/549i61292935343.ps (open in new window)

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ;

R code (references can be found in the software module):

par1 <- as.numeric(par1)

nx <- length(x)

x <- ts(x,frequency=par1)

m <- StructTS(x,type='BSM')

m$coef

m$fitted

m$resid

mylevel <- as.numeric(m$fitted[,'level'])

myslope <- as.numeric(m$fitted[,'slope'])

myseas <- as.numeric(m$fitted[,'sea'])

myresid <- as.numeric(m$resid)

myfit <- mylevel+myseas

mylagmax <- nx/2

bitmap(file='test2.png')

op <- par(mfrow = c(2,2))

acf(as.numeric(x),lag.max = mylagmax,main='Observed')

acf(mylevel,na.action=na.pass,lag.max = mylagmax,main='Level')

acf(myseas,na.action=na.pass,lag.max = mylagmax,main='Seasonal')

acf(myresid,na.action=na.pass,lag.max = mylagmax,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test3.png')

op <- par(mfrow = c(2,2))

spectrum(as.numeric(x),main='Observed')

spectrum(mylevel,main='Level')

spectrum(myseas,main='Seasonal')

spectrum(myresid,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test4.png')

op <- par(mfrow = c(2,2))

cpgram(as.numeric(x),main='Observed')

cpgram(mylevel,main='Level')

cpgram(myseas,main='Seasonal')

cpgram(myresid,main='Standardized Residals')

par(op)

dev.off()

bitmap(file='test1.png')

plot(as.numeric(m$resid),main='Standardized Residuals',ylab='Residuals',xlab='time',type='b')

grid()

dev.off()

bitmap(file='test5.png')

op <- par(mfrow = c(2,2))

hist(m$resid,main='Residual Histogram')

plot(density(m$resid),main='Residual Kernel Density')

qqnorm(m$resid,main='Residual Normal QQ Plot')

qqline(m$resid)

plot(m$resid^2, myfit^2,main='Sq.Resid vs. Sq.Fit',xlab='Squared residuals',ylab='Squared Fit')

par(op)

dev.off()

load(file='createtable')

a<-table.start()

a<-table.row.start(a)

a<-table.element(a,'Structural Time Series Model',6,TRUE)

a<-table.row.end(a)

a<-table.row.start(a)

a<-table.element(a,'t',header=TRUE)

a<-table.element(a,'Observed',header=TRUE)

a<-table.element(a,'Level',header=TRUE)

a<-table.element(a,'Slope',header=TRUE)

a<-table.element(a,'Seasonal',header=TRUE)

a<-table.element(a,'Stand. Residuals',header=TRUE)

a<-table.row.end(a)

for (i in 1:nx) {

a<-table.row.start(a)

a<-table.element(a,i,header=TRUE)

a<-table.element(a,x[i])

a<-table.element(a,mylevel[i])

a<-table.element(a,myslope[i])

a<-table.element(a,myseas[i])

a<-table.element(a,myresid[i])

a<-table.row.end(a)

}

a<-table.end(a)

table.save(a,file='mytable.tab')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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